KPSS-test
#import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import kpss
# Generate synthetic stationary and non-stationary data
np.random.seed(17)
# Stationary data: White noise
stationary_data = np.random.normal(size=100)
# Create a random walk with larger step size to make it more volatile
random_walk = np.cumsum(np.random.normal(scale=2, size=n)) # Increase the scale for larger volatility
trend = np.linspace(0, 30, n) # Add a strong linear trend (larger trend)
# Combine random walk and trend for clear non-stationary behavior
non_stationary_data = random_walk + trend
# Plot the data
plt.figure(figsize=(10,5))
plt.subplot(1, 2, 1)
plt.plot(stationary_data)
plt.title('Stationary Data')
plt.subplot(1, 2, 2)
plt.plot(non_stationary_data)
plt.title('Non-Stationary Data')
plt.tight_layout()
plt.show()
parts of the ADF test –
tuple
result = kpss(stationary_data)
print(result)
access by index
print('ADF Test Statistic:', result[0])
print('p-value:', result[1])
print('Number of Lags Used:', result[2])
print('Critical Values:', result[3])
adf_stat, p_value, lags, n_obs = result
print(adf_stat)
# Function to perform ADF test
def kpss_test(series):
result = kpss(series)
print(f'p-value: {result[1]}')
if result[1] <= 0.05:
print("=> Strong evidence against the null hypothesis, reject the null hypothesis. Data is non-stationary.")
else:
print("=> Weak evidence against the null hypothesis, fail to reject the null hypothesis. Data is level or trend stationary.")
kpss_test(stationary_data)
kpss_test(non_stationary_data)
